1. IMPORT ALL LIBRARIES¶

In [ ]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.tsa.stattools import adfuller
from sklearn.metrics import mean_absolute_error, r2_score
from sklearn.ensemble import RandomForestRegressor
from sklearn.preprocessing import StandardScaler
import warnings
warnings.filterwarnings("ignore")

2. LOAD THE DATASET¶

In [ ]:
data = pd.read_excel('./Surface Water Data Bulbul  Guaging Station 1995-2021 Final.xlsx')
data.head()
Out[ ]:
Year Station Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0 1995 Bulbul 1.0 0.593 0.47 0.470 0.393 4.741 4.37 3.174 3.445 2.965 4.007 4.443 3.377
1 1995 Bulbul 2.0 0.593 0.47 0.470 0.356 5.120 4.151 3.723 4.443 3.25 4.007 4.296 3.309
2 1995 Bulbul 3.0 0.593 0.47 0.593 0.356 5.197 3.794 4.151 4.443 3.552 3.723 4.37 3.309
3 1995 Bulbul 4.0 0.593 0.47 0.678 0.51 5.044 2.778 3.794 4.223 4.113 3.671 4.591 3.241
4 1995 Bulbul 5.0 0.593 0.47 0.767 0.51 6.306 2.523 3.309 4.007 4.22 3.589 4.517 3.174
In [ ]:
# List of stations to keep
stations_to_keep = ["Mean", "Flow (MCM)", "Maximum", "Minimum", "Runoff (mm)"]

# Filter the dataframe
filtered_df = data[data["Station "].isin(stations_to_keep)]
filtered_df.tail()
Out[ ]:
Year Station Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
966 2021 Mean NaN 0.713 0.316 0.243 0.244 1.091 3.972 17.180 25.200 21.008 8.25 3.015 0.534
967 2021 Flow (MCM) NaN 1.909 0.765 0.650 0.634 2.921 10.297 15.332 10.440 16.683 22.096 7.814 1.431
968 2021 Maximum NaN 0.994 0.418 0.341 0.356 2.744 5.738 2.866 2.672 2.785 11.999 4.806 1.172
969 2021 Minimum NaN 0.434 0.233 0.160 0.144 0.231 2.93 2.590 2.530 2.611 4.961 1.366 0.248
970 2021 Runoff (mm) NaN 3.629 1.454 1.236 1.205 5.553 19.575 20.257 21.122 22.661 42.008 14.855 2.721
In [ ]:
filtered_df.rename(columns={'Station ':'Parameter'}, inplace=True)
filtered_df.drop(columns={'Day '}, inplace=True)
filtered_df.head()
Out[ ]:
Year Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
31 1995 Mean 0.460 0.555 0.511 2.048 3.435 2.117 3.487 3.637 3.489 3.671 3.808 3.597
32 1995 Flow (MCM) 1.231 1.343 1.370 5.309 9.200 5.486 9.341 9.623 9.578 9.672 9.871 9.633
33 1995 Maximum 0.593 0.722 1.002 6.966 6.306 4.37 4.151 4.593 4.452 4.471 4.591 5.044
34 1995 Minimum 0.356 0.47 0.286 0.286 1.202 0.954 2.398 2.965 2.965 1.151 1.151 3.174
35 1995 Runoff (mm) 2.340 2.553 2.604 10.093 17.491 10.43 17.758 17.549 17.2 17.034 18.766 18.314

3. TRANSFORM THE DATASET¶

In [ ]:
# Remove extra spaces
filtered_df.columns = filtered_df.columns.str.strip()
filtered_df.head()
Out[ ]:
Year Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
31 1995 Mean 0.460 0.555 0.511 2.048 3.435 2.117 3.487 3.637 3.489 3.671 3.808 3.597
32 1995 Flow (MCM) 1.231 1.343 1.370 5.309 9.200 5.486 9.341 9.623 9.578 9.672 9.871 9.633
33 1995 Maximum 0.593 0.722 1.002 6.966 6.306 4.37 4.151 4.593 4.452 4.471 4.591 5.044
34 1995 Minimum 0.356 0.47 0.286 0.286 1.202 0.954 2.398 2.965 2.965 1.151 1.151 3.174
35 1995 Runoff (mm) 2.340 2.553 2.604 10.093 17.491 10.43 17.758 17.549 17.2 17.034 18.766 18.314
In [ ]:
filtered_df.columns
Out[ ]:
Index(['Year', 'Parameter', 'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul',
       'Aug', 'Sep', 'Oct', 'Nov', 'Dec'],
      dtype='object')
In [ ]:
def transform_data(df):
    # Melt the dataframe
    melted_df = df.melt(id_vars=["Parameter", "Year"],
                        value_vars=["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"],
                        var_name="Month", value_name="Value")

    # Map month names to numbers
    month_mapping = {
        "Jan": "01", "Feb": "02", "Mar": "03", "Apr": "04", "May": "05", "Jun": "06",
        "Jul": "07", "Aug": "08", "Sep": "09", "Oct": "10", "Nov": "11", "Dec": "12"
    }
    melted_df["Month"] = melted_df["Month"].map(month_mapping)

    # Combine Year and Month into a Date column
    melted_df["Date"] = pd.to_datetime(melted_df["Year"].astype(str) + "-" + melted_df["Month"] + "-01")

    # Select and reorder the final columns
    transformed_df = melted_df[["Parameter", "Date", "Value"]]

    return transformed_df
In [ ]:
# Transform the data
transformed_data = transform_data(filtered_df)
In [ ]:
transformed_data.head()
Out[ ]:
Parameter Date Value
0 Mean 1995-01-01 0.46
1 Flow (MCM) 1995-01-01 1.231
2 Maximum 1995-01-01 0.593
3 Minimum 1995-01-01 0.356
4 Runoff (mm) 1995-01-01 2.34
In [ ]:
# UNIQUE VALUES ONLY
unique_parameters = transformed_data['Parameter'].unique()
In [ ]:
for value in transformed_data['Value']:
    if isinstance(value, (int, float)):
        continue
    else:
        print(value)
In [ ]:
transformed_data.Value.isnull().sum()
Out[ ]:
0
In [ ]:
# Convert 'Value' column to float
transformed_data['Value'] = transformed_data['Value'].astype(float)
In [ ]:
# RENAMA THE PARAMETERS
rename_dict = {
    unique_parameters[0]: 'Mean Flow',
    unique_parameters[1]: 'FLow',
    unique_parameters[2]: 'Max FLow',
    unique_parameters[3]: 'Min Flow',
    unique_parameters[4]: 'Runoff'
}

# Renaming the parameters
transformed_data['Parameter'] = transformed_data['Parameter'].replace(rename_dict)
transformed_data.head()
Out[ ]:
Parameter Date Value
0 Mean Flow 1995-01-01 0.460
1 FLow 1995-01-01 1.231
2 Max FLow 1995-01-01 0.593
3 Min Flow 1995-01-01 0.356
4 Runoff 1995-01-01 2.340
In [ ]:
# Parameter counts
transformed_data.Parameter.value_counts()
Out[ ]:
Parameter
Mean Flow    324
FLow         324
Max FLow     324
Min Flow     324
Runoff       312
Name: count, dtype: int64

4. PLOT VALUES OF EACH PARAMETERS¶

In [ ]:
parameters = transformed_data['Parameter'].unique()

custom_colors = {
    parameters[0]: '#2ca02c',
    parameters[1]: '#8b0000',
    parameters[2]: '#ff6347',
    parameters[3]: '#8c564b',
    parameters[4]: '#ff7f0e',
}

plt.figure(figsize=(40, 10))

for parameter in parameters:
    parameter_data = transformed_data[transformed_data['Parameter'] == parameter]
    parameter_data.set_index('Date', inplace=True)
    sns.lineplot(data=parameter_data,
                 x=parameter_data.index,
                 y='Value',
                 marker='o',
                 label=parameter,
                 linewidth=1,
                 color=custom_colors[parameter])

# plt.title('Monthly Analysis', fontsize=24)
plt.xlabel('Date', fontsize=24)
plt.ylabel('Streamflow(m3/s)', fontsize=26)
plt.legend(loc='best', fontsize=24, framealpha=0.5)
plt.xticks(fontsize=24)
plt.yticks(fontsize=24)
plt.show()
No description has been provided for this image
In [ ]:
parameters = transformed_data['Parameter'].unique()
parameters
Out[ ]:
array(['Mean Flow', 'FLow', 'Max FLow', 'Min Flow', 'Runoff'],
      dtype=object)

5. FIND THE CORRELATIONS BETWEEN EACH PARAMETERS¶

In [ ]:
# Assuming transformed_data is already defined
pivot_data = transformed_data.pivot(index='Date', columns='Parameter', values='Value')
correlation_matrix = pivot_data.corr()

plt.figure(figsize=(16, 10))
sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', square=True, linewidths=0.5, annot_kws={"size": 18})

# Adjust x-tick and y-tick labels rotation
plt.xticks(rotation=90, fontsize=20)
plt.yticks(rotation=0, fontsize=20)

plt.xlabel('')
plt.ylabel('')
plt.show()
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6. COMMON FUNCTION¶

TIME SERIES TO SUPERVISED¶

In [ ]:
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
    n_vars = 1 if type(data) is list else data.shape[1]
    df = pd.DataFrame(data)
    cols = []
    for i in range(n_in, 0, -1):
        cols.append(df.shift(i))
    for i in range(0, n_out):
        cols.append(df.shift(-i))
    agg = pd.concat(cols, axis=1)
    if dropnan:
        agg.dropna(inplace=True)
    return agg.values

ADD ROLLING FEATURES¶

In [ ]:
def add_rolling_features(data, window=3):
    df = pd.DataFrame(data)
    df['rolling_mean'] = df.iloc[:, 0].rolling(window=window).mean()
    df['rolling_std'] = df.iloc[:, 0].rolling(window=window).std()
    df.dropna(inplace=True)
    return df

TRAIN TEST SPLITT¶

In [ ]:
def train_test_split(data, train_size=0.9):
    n_train = int(len(data) * train_size)
    return data[:n_train], data[n_train:]

MEASURING METRICS¶

In [ ]:
def nash_sutcliffe_efficiency(y_true, y_pred):
    return 1 - (np.sum((y_true - y_pred)**2) / np.sum((y_true - np.mean(y_true))**2))
def willmotts_index(y_true, y_pred):
    return 1 - (np.sum((y_pred - y_true)**2) / np.sum((np.abs(y_pred - np.mean(y_true)) + np.abs(y_true - np.mean(y_true)))**2))

CROSS VALIDATION AND MODEL EVALUATIONS¶

In [ ]:
def walk_forward_validation(data, model):
    predictions = []
    train, test = train_test_split(data)
    history = [x for x in train.values]
    for i in range(len(test)):
        testX, testy = test.iloc[i, :-1].values, test.iloc[i, -1]
        yhat = model(history, testX)
        predictions.append(yhat)
        history.append(test.iloc[i].values)
        print('>expected=%.1f, predicted=%.1f' % (testy, yhat))
    mae = mean_absolute_error(test.iloc[:, -1], predictions)
    rmse = np.sqrt(np.mean((test.iloc[:, -1] - np.asarray(predictions))**2))
    r2 = r2_score(test.iloc[:, -1], predictions)
    nse = nash_sutcliffe_efficiency(test.iloc[:, -1], predictions)
    willmott = willmotts_index(test.iloc[:, -1], predictions)
    return mae, rmse, r2, nse, willmott, test.index, test.iloc[:, -1], predictions

7. MODELS¶

1. RANDOM FOREST¶

In [ ]:
def random_forest_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = RandomForestRegressor(n_estimators=50)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

2. SVM¶

In [ ]:
from sklearn.svm import SVR
def svm_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = SVR(kernel='rbf')
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

3. XGBRegressor¶

In [ ]:
from xgboost import XGBRegressor
def xgboost_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = XGBRegressor(n_estimators=50)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

4. LGBMRegressor¶

In [ ]:
from lightgbm import LGBMRegressor
def lightgbm_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = LGBMRegressor(n_estimators=50, verbose=-1)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]
In [ ]:
# Color dictionary for different models
colors_dict = {
    'LightGBM': '#27ad81',
    'XGBoost': '#5dc863',
    'SVM': '#aadc32',
    'Random Forest': '#fde725'
}

6. MEAN FLOW ANALYSIS¶

In [ ]:
# Get the mean flow values
mean_flow = transformed_data[transformed_data['Parameter'] == parameters[0]]
mean_flow.head()
Out[ ]:
Parameter Date Value
0 Mean Flow 1995-01-01 0.460
5 Mean Flow 1996-01-01 1.084
10 Mean Flow 1997-01-01 0.867
15 Mean Flow 1998-01-01 2.006
20 Mean Flow 1999-01-01 2.389
In [ ]:
# drop the parameter columns
mean_flow = mean_flow.drop(columns=['Parameter'])
In [ ]:
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.460
5 1996-01-01 1.084
10 1997-01-01 0.867
15 1998-01-01 2.006
20 1999-01-01 2.389
In [ ]:
# sort according to  the date
mean_flow= mean_flow.sort_values(by='Date')
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.460
134 1995-02-01 0.555
268 1995-03-01 0.511
402 1995-04-01 2.048
536 1995-05-01 3.435
In [ ]:
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.460
134 1995-02-01 0.555
268 1995-03-01 0.511
402 1995-04-01 2.048
536 1995-05-01 3.435
In [ ]:
plt.figure(figsize=(20, 8))
mean_flow.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#2ca02c', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Mean Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
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In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(mean_flow['Value'])

ADF Test Statistic : -4.046217573308878
p-value : 0.001186928991902695
#Lags Used : 13
Number of Observations Used : 310
Strong evidence against the null hypothesis(H0)
In [ ]:
mean_flow = mean_flow[['Date', 'Value']]
mean_flow.set_index('Date', inplace=True)
mean_flow.head()
Out[ ]:
Value
Date
1995-01-01 0.460
1995-02-01 0.555
1995-03-01 0.511
1995-04-01 2.048
1995-05-01 3.435
In [ ]:
model_names = []
mae_values = []
rmse_values = []
r2_values = []
nse_values = []
willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `mean flow` is your time series DataFrame
series = mean_flow
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



# Plot predictions for each model
for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Mean Flow(m3/s)', fontsize=18)
plt.legend(fontsize=14, loc='upper center', bbox_to_anchor=(0.6, 1.15), ncol=1)
plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.4
>expected=0.8, predicted=0.8
>expected=0.1, predicted=0.2
>expected=-0.3, predicted=0.2
>expected=-0.2, predicted=0.2
>expected=1.3, predicted=1.3
>expected=1.1, predicted=1.2
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.9
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.6
>expected=0.6, predicted=0.4
>expected=-0.3, predicted=0.2
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.2
>expected=-0.1, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.5
>expected=0.9, predicted=1.1
>expected=-0.2, predicted=-0.0
>expected=0.6, predicted=-0.2
>expected=0.7, predicted=0.8
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.4
>expected=0.8, predicted=0.6
>expected=0.1, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=0.3
>expected=1.3, predicted=1.2
>expected=1.1, predicted=1.0
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.5
>expected=0.9, predicted=0.8
>expected=0.6, predicted=0.6
>expected=-0.3, predicted=0.3
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.4
>expected=-0.1, predicted=-0.0
>expected=0.2, predicted=0.3
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.7
>expected=0.9, predicted=1.1
>expected=-0.2, predicted=0.1
>expected=0.6, predicted=0.0
>expected=0.7, predicted=0.6
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.2
>expected=0.8, predicted=0.9
>expected=0.1, predicted=0.4
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=0.2
>expected=1.3, predicted=1.2
>expected=1.1, predicted=1.1
>expected=-0.6, predicted=-0.4
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.7
>expected=0.6, predicted=0.5
>expected=-0.3, predicted=0.1
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.0
>expected=-0.1, predicted=-0.3
>expected=0.2, predicted=-0.1
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.5
>expected=0.9, predicted=1.0
>expected=-0.2, predicted=0.1
>expected=0.6, predicted=0.5
>expected=0.7, predicted=0.8
>expected=-0.2, predicted=-0.2
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.7
>expected=0.8, predicted=0.9
>expected=0.1, predicted=0.4
>expected=-0.3, predicted=0.3
>expected=-0.2, predicted=0.5
>expected=1.3, predicted=1.1
>expected=1.1, predicted=0.9
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.7
>expected=0.6, predicted=0.5
>expected=-0.3, predicted=0.3
>expected=-0.2, predicted=0.2
>expected=-0.3, predicted=0.4
>expected=-0.1, predicted=0.4
>expected=0.2, predicted=0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=0.6, predicted=0.6
>expected=0.9, predicted=0.9
>expected=-0.2, predicted=0.2
>expected=0.6, predicted=0.3
>expected=0.7, predicted=0.7
>expected=-0.2, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.4
>expected=0.8, predicted=0.8
>expected=0.1, predicted=0.2
>expected=-0.3, predicted=0.2
>expected=-0.2, predicted=0.2
>expected=1.3, predicted=1.3
>expected=1.1, predicted=1.2
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.9
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.6
>expected=0.6, predicted=0.4
>expected=-0.3, predicted=0.2
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.2
>expected=-0.1, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.5
>expected=0.9, predicted=1.1
>expected=-0.2, predicted=-0.0
>expected=0.6, predicted=-0.2
>expected=0.7, predicted=0.8
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.4
>expected=0.8, predicted=0.6
>expected=0.1, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=0.3
>expected=1.3, predicted=1.2
>expected=1.1, predicted=1.0
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.5
>expected=0.9, predicted=0.8
>expected=0.6, predicted=0.6
>expected=-0.3, predicted=0.3
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.4
>expected=-0.1, predicted=-0.0
>expected=0.2, predicted=0.3
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.7
>expected=0.9, predicted=1.1
>expected=-0.2, predicted=0.1
>expected=0.6, predicted=0.0
>expected=0.7, predicted=0.6
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.2
>expected=0.8, predicted=0.9
>expected=0.1, predicted=0.4
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=0.2
>expected=1.3, predicted=1.2
>expected=1.1, predicted=1.1
>expected=-0.6, predicted=-0.4
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.7
>expected=0.6, predicted=0.5
>expected=-0.3, predicted=0.1
>expected=-0.2, predicted=0.1
>expected=-0.3, predicted=0.0
>expected=-0.1, predicted=-0.3
>expected=0.2, predicted=-0.1
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.6, predicted=0.5
>expected=0.9, predicted=1.0
>expected=-0.2, predicted=0.1
>expected=0.6, predicted=0.5
>expected=0.7, predicted=0.8
>expected=-0.2, predicted=-0.2
>expected=-0.6, predicted=-0.6
>expected=0.3, predicted=0.6
>expected=0.8, predicted=0.8
>expected=0.1, predicted=0.3
>expected=-0.3, predicted=0.2
>expected=-0.2, predicted=0.5
>expected=1.3, predicted=1.2
>expected=1.1, predicted=1.0
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=0.9, predicted=0.6
>expected=0.6, predicted=0.5
>expected=-0.3, predicted=0.4
>expected=-0.2, predicted=0.2
>expected=-0.3, predicted=0.3
>expected=-0.1, predicted=0.2
>expected=0.2, predicted=0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=0.6, predicted=0.6
>expected=0.9, predicted=0.9
>expected=-0.2, predicted=0.2
>expected=0.6, predicted=0.3
>expected=0.7, predicted=0.7
>expected=-0.2, predicted=-0.5
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.159064 0.254459 0.844434 0.844434 0.960785
1 XGBoost 0.152257 0.238392 0.863459 0.863459 0.964632
2 SVM 0.128908 0.174601 0.926756 0.926756 0.981072
3 Random Forest 0.193570 0.291132 0.796362 0.796362 0.948670
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Mean Flow')
plt.show()
No description has been provided for this image
In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
No description has been provided for this image
No description has been provided for this image
No description has been provided for this image
No description has been provided for this image
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7. FLOW ANALYSIS¶

In [ ]:
# Get the temp_max values
flow = transformed_data[transformed_data['Parameter'] == parameters[1]]
flow.head()
Out[ ]:
Parameter Date Value
1 FLow 1995-01-01 1.231
6 FLow 1996-01-01 33.074
11 FLow 1997-01-01 2.322
16 FLow 1998-01-01 5.372
21 FLow 1999-01-01 6.398
In [ ]:
# drop the parameter columns
flow = flow.drop(columns=['Parameter'])
In [ ]:
flow.head()
Out[ ]:
Date Value
1 1995-01-01 1.231
6 1996-01-01 33.074
11 1997-01-01 2.322
16 1998-01-01 5.372
21 1999-01-01 6.398
In [ ]:
# sort according to  the date
flow= flow.sort_values(by='Date')
flow.head()
Out[ ]:
Date Value
1 1995-01-01 1.231
135 1995-02-01 1.343
269 1995-03-01 1.370
403 1995-04-01 5.309
537 1995-05-01 9.200
In [ ]:
flow.head()
Out[ ]:
Date Value
1 1995-01-01 1.231
135 1995-02-01 1.343
269 1995-03-01 1.370
403 1995-04-01 5.309
537 1995-05-01 9.200
In [ ]:
plt.figure(figsize=(20, 8))
flow.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#8b0000', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow['Value'])

ADF Test Statistic : -3.1388896550094847
p-value : 0.023805869554636105
#Lags Used : 13
Number of Observations Used : 310
Strong evidence against the null hypothesis(H0)
In [ ]:
flow = flow[['Date', 'Value']]
flow.set_index('Date', inplace=True)
flow.head()
Out[ ]:
Value
Date
1995-01-01 1.231
1995-02-01 1.343
1995-03-01 1.370
1995-04-01 5.309
1995-05-01 9.200
In [ ]:
flow_model_names = []
flow_mae_values = []
flow_rmse_values = []
flow_r2_values = []
flow_nse_values = []
flow_willmott_values = []

TRAIN THE MODELS¶

In [ ]:
# Assuming `temp_max` is your time series DataFrame
series = flow
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.0, predicted=0.2
>expected=-0.0, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=-0.2
>expected=-0.3, predicted=-0.0
>expected=-0.7, predicted=-0.0
>expected=-0.7, predicted=-0.3
>expected=-0.0, predicted=-0.2
>expected=0.1, predicted=-0.1
>expected=0.4, predicted=0.2
>expected=-0.4, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=-0.3, predicted=-0.4
>expected=-0.2, predicted=0.0
>expected=-0.0, predicted=-0.1
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.3
>expected=-0.5, predicted=-0.1
>expected=-0.0, predicted=0.5
>expected=-0.0, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=0.0
>expected=-0.3, predicted=0.3
>expected=-0.7, predicted=0.1
>expected=-0.7, predicted=-0.3
>expected=-0.0, predicted=-0.3
>expected=0.1, predicted=0.1
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.5
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=0.1
>expected=-0.0, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.3
>expected=0.2, predicted=0.1
>expected=-0.3, predicted=-0.0
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.0
>expected=-0.0, predicted=0.0
>expected=-0.0, predicted=-0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.1, predicted=-0.1
>expected=-0.3, predicted=-0.1
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.0, predicted=0.1
>expected=0.1, predicted=-0.1
>expected=0.4, predicted=0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.4
>expected=-0.3, predicted=-0.3
>expected=-0.2, predicted=-0.4
>expected=-0.0, predicted=-0.4
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.6
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.2
>expected=-0.0, predicted=0.4
>expected=-0.0, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=0.0
>expected=-0.3, predicted=0.2
>expected=-0.7, predicted=0.0
>expected=-0.7, predicted=-0.1
>expected=-0.0, predicted=0.1
>expected=0.1, predicted=0.1
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.3
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.0, predicted=0.2
>expected=-0.0, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=-0.2
>expected=-0.3, predicted=-0.0
>expected=-0.7, predicted=-0.0
>expected=-0.7, predicted=-0.3
>expected=-0.0, predicted=-0.2
>expected=0.1, predicted=-0.1
>expected=0.4, predicted=0.2
>expected=-0.4, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=-0.3, predicted=-0.4
>expected=-0.2, predicted=0.0
>expected=-0.0, predicted=-0.1
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.4
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.3
>expected=-0.5, predicted=-0.1
>expected=-0.0, predicted=0.5
>expected=-0.0, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=0.0
>expected=-0.3, predicted=0.3
>expected=-0.7, predicted=0.1
>expected=-0.7, predicted=-0.3
>expected=-0.0, predicted=-0.3
>expected=0.1, predicted=0.1
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.5
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=0.1
>expected=-0.0, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.3
>expected=0.2, predicted=0.1
>expected=-0.3, predicted=-0.0
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.0
>expected=-0.0, predicted=0.0
>expected=-0.0, predicted=-0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.1, predicted=-0.1
>expected=-0.3, predicted=-0.1
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.0, predicted=0.1
>expected=0.1, predicted=-0.1
>expected=0.4, predicted=0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.4
>expected=-0.3, predicted=-0.3
>expected=-0.2, predicted=-0.4
>expected=-0.0, predicted=-0.4
>expected=-0.5, predicted=-0.5
>expected=0.5, predicted=0.5
>expected=0.2, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.3
>expected=-0.5, predicted=-0.2
>expected=-0.0, predicted=0.4
>expected=-0.0, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.1, predicted=-0.1
>expected=-0.3, predicted=0.2
>expected=-0.7, predicted=-0.0
>expected=-0.7, predicted=-0.2
>expected=-0.0, predicted=-0.1
>expected=0.1, predicted=0.1
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.158344 0.222436 0.533140 0.533140 0.880003
1 XGBoost 0.171128 0.264562 0.339568 0.339568 0.846199
2 SVM 0.130814 0.178804 0.698332 0.698332 0.904694
3 Random Forest 0.146455 0.231957 0.492320 0.492320 0.885462
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Flow')
plt.show()
No description has been provided for this image
In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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8. MAX FLOW ANALYSIS¶

In [ ]:
# Get the temp_max values
flow_max = transformed_data[transformed_data['Parameter'] == parameters[2]]
flow_max.head()
Out[ ]:
Parameter Date Value
2 Max FLow 1995-01-01 0.593
7 Max FLow 1996-01-01 23.131
12 Max FLow 1997-01-01 1.358
17 Max FLow 1998-01-01 3.377
22 Max FLow 1999-01-01 43.585
In [ ]:
# drop the parameter columns
flow_max = flow_max.drop(columns=['Parameter'])
In [ ]:
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.593
7 1996-01-01 23.131
12 1997-01-01 1.358
17 1998-01-01 3.377
22 1999-01-01 43.585
In [ ]:
# sort according to  the date
flow_max= flow_max.sort_values(by='Date')
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.593
136 1995-02-01 0.722
270 1995-03-01 1.002
404 1995-04-01 6.966
538 1995-05-01 6.306
In [ ]:
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.593
136 1995-02-01 0.722
270 1995-03-01 1.002
404 1995-04-01 6.966
538 1995-05-01 6.306
In [ ]:
plt.figure(figsize=(20, 8))
flow_max.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#ff6347', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Max Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
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In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow_max['Value'])

ADF Test Statistic : -2.792227314758844
p-value : 0.05939264708899431
#Lags Used : 11
Number of Observations Used : 312
Weak evidence against the null hypothesis(H0)
In [ ]:
flow_max = flow_max[['Date', 'Value']]
flow_max.set_index('Date', inplace=True)
flow_max.head()
Out[ ]:
Value
Date
1995-01-01 0.593
1995-02-01 0.722
1995-03-01 1.002
1995-04-01 6.966
1995-05-01 6.306
In [ ]:
flow_max_model_names = []
flow_max_mae_values = []
flow_max_rmse_values = []
flow_max_r2_values = []
flow_max_nse_values = []
flow_max_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `flow_max` is your time series DataFrame
series = flow_max
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Max Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)
plt.grid(axis='y', linestyle='--')
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

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>expected=-0.5, predicted=0.1
>expected=-0.8, predicted=0.1
>expected=-0.5, predicted=0.0
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>expected=0.4, predicted=0.2
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>expected=-0.3, predicted=-0.2
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>expected=-0.4, predicted=-0.1
>expected=-0.2, predicted=-0.0
>expected=-0.3, predicted=0.8
>expected=0.4, predicted=0.1
>expected=0.7, predicted=0.7
>expected=-0.1, predicted=-0.1
>expected=-0.6, predicted=-0.6
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>expected=-0.8, predicted=-0.8
>expected=-0.3, predicted=-0.4
>expected=-0.1, predicted=0.2
>expected=-0.5, predicted=-0.0
>expected=-0.8, predicted=-0.0
>expected=-0.5, predicted=-0.1
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>expected=0.2, predicted=0.1
>expected=0.4, predicted=0.1
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.7
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>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.8, predicted=-0.7
>expected=-0.3, predicted=-0.2
>expected=-0.4, predicted=-0.2
>expected=-0.3, predicted=-0.3
>expected=-0.6, predicted=-0.6
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>expected=0.3, predicted=0.2
>expected=-0.4, predicted=-0.1
>expected=-0.2, predicted=0.0
>expected=-0.3, predicted=-0.1
>expected=0.4, predicted=0.2
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>expected=-0.6, predicted=-0.6
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>expected=-0.2, predicted=0.1
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>expected=-0.3, predicted=-0.1
>expected=-0.4, predicted=-0.0
>expected=-0.3, predicted=-0.2
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.170838 0.282477 0.486516 0.486516 0.874883
1 XGBoost 0.142425 0.229764 0.660276 0.660276 0.915196
2 SVM 0.140103 0.192508 0.761515 0.761515 0.932628
3 Random Forest 0.151488 0.244824 0.614283 0.614283 0.906754
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Max Flow')
plt.show()
No description has been provided for this image
In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
No description has been provided for this image
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9. MIN FLOW ANALYSIS¶

In [ ]:
flow_min = transformed_data[transformed_data['Parameter']=='Min Flow']
In [ ]:
# drop the parameter columns
flow_min = flow_min.drop(columns=['Parameter'])
In [ ]:
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.356
8 1996-01-01 5.983
13 1997-01-01 0.593
18 1998-01-01 1.254
23 1999-01-01 0.813
In [ ]:
# sort according to  the date
flow_min = flow_min.sort_values(by='Date')
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.356
137 1995-02-01 0.470
271 1995-03-01 0.286
405 1995-04-01 0.286
539 1995-05-01 1.202
In [ ]:
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.356
137 1995-02-01 0.470
271 1995-03-01 0.286
405 1995-04-01 0.286
539 1995-05-01 1.202
In [ ]:
plt.figure(figsize=(20, 8))
flow_min.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#8c564b', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Min Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow_min['Value'])

ADF Test Statistic : -3.9056974671331663
p-value : 0.0019933147027447386
#Lags Used : 11
Number of Observations Used : 312
Strong evidence against the null hypothesis(H0)
In [ ]:
flow_min = flow_min[['Date', 'Value']]
flow_min.set_index('Date', inplace=True)
flow_min.head()
Out[ ]:
Value
Date
1995-01-01 0.356
1995-02-01 0.470
1995-03-01 0.286
1995-04-01 0.286
1995-05-01 1.202
In [ ]:
flow_min_model_names = []
flow_min_mae_values = []
flow_min_rmse_values = []
flow_min_r2_values = []
flow_min_nse_values = []
flow_min_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `flow min` is your time series DataFrame
series = flow_min
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Min Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=0.0
>expected=0.7, predicted=1.1
>expected=1.2, predicted=1.6
>expected=0.4, predicted=0.4
>expected=1.5, predicted=1.5
>expected=1.3, predicted=1.0
>expected=-0.3, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.7
>expected=0.9, predicted=1.1
>expected=-0.7, predicted=1.3
>expected=-0.0, predicted=0.9
>expected=-0.1, predicted=0.4
>expected=-0.1, predicted=-0.2
>expected=0.1, predicted=0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=-0.2
>expected=-0.0, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=0.0
>expected=0.7, predicted=1.1
>expected=1.2, predicted=1.1
>expected=0.4, predicted=-0.1
>expected=1.5, predicted=1.6
>expected=1.3, predicted=1.4
>expected=-0.3, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.5
>expected=0.9, predicted=0.9
>expected=-0.7, predicted=1.0
>expected=-0.0, predicted=0.4
>expected=-0.1, predicted=0.2
>expected=-0.1, predicted=-0.2
>expected=0.1, predicted=0.2
>expected=-0.4, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.3
>expected=-0.3, predicted=-0.4
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.3, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
>expected=-0.6, predicted=-0.5
>expected=-0.0, predicted=-0.1
>expected=0.7, predicted=0.8
>expected=1.2, predicted=1.4
>expected=0.4, predicted=0.8
>expected=1.5, predicted=1.7
>expected=1.3, predicted=1.6
>expected=-0.3, predicted=-0.4
>expected=-0.6, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=0.9, predicted=0.7
>expected=0.9, predicted=1.0
>expected=-0.7, predicted=0.4
>expected=-0.0, predicted=0.3
>expected=-0.1, predicted=0.7
>expected=-0.1, predicted=0.2
>expected=0.1, predicted=-0.1
>expected=-0.4, predicted=-0.3
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.3, predicted=-0.3
>expected=-0.3, predicted=-0.3
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=-0.4
>expected=-0.0, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=-0.0
>expected=0.7, predicted=1.5
>expected=1.2, predicted=1.4
>expected=0.4, predicted=0.9
>expected=1.5, predicted=1.3
>expected=1.3, predicted=1.2
>expected=-0.3, predicted=-0.2
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.6
>expected=0.9, predicted=1.4
>expected=-0.7, predicted=0.8
>expected=-0.0, predicted=0.8
>expected=-0.1, predicted=0.8
>expected=-0.1, predicted=-0.2
>expected=0.1, predicted=-0.0
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.1
>expected=-0.7, predicted=-0.4
>expected=-0.3, predicted=-0.3
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=0.0
>expected=0.7, predicted=1.1
>expected=1.2, predicted=1.6
>expected=0.4, predicted=0.4
>expected=1.5, predicted=1.5
>expected=1.3, predicted=1.0
>expected=-0.3, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.7
>expected=0.9, predicted=1.1
>expected=-0.7, predicted=1.3
>expected=-0.0, predicted=0.9
>expected=-0.1, predicted=0.4
>expected=-0.1, predicted=-0.2
>expected=0.1, predicted=0.1
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=-0.2
>expected=-0.0, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=0.0
>expected=0.7, predicted=1.1
>expected=1.2, predicted=1.1
>expected=0.4, predicted=-0.1
>expected=1.5, predicted=1.6
>expected=1.3, predicted=1.4
>expected=-0.3, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.5
>expected=0.9, predicted=0.9
>expected=-0.7, predicted=1.0
>expected=-0.0, predicted=0.4
>expected=-0.1, predicted=0.2
>expected=-0.1, predicted=-0.2
>expected=0.1, predicted=0.2
>expected=-0.4, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.3
>expected=-0.3, predicted=-0.4
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.3, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
>expected=-0.6, predicted=-0.5
>expected=-0.0, predicted=-0.1
>expected=0.7, predicted=0.8
>expected=1.2, predicted=1.4
>expected=0.4, predicted=0.8
>expected=1.5, predicted=1.7
>expected=1.3, predicted=1.6
>expected=-0.3, predicted=-0.4
>expected=-0.6, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=0.9, predicted=0.7
>expected=0.9, predicted=1.0
>expected=-0.7, predicted=0.4
>expected=-0.0, predicted=0.3
>expected=-0.1, predicted=0.7
>expected=-0.1, predicted=0.2
>expected=0.1, predicted=-0.1
>expected=-0.4, predicted=-0.3
>expected=-0.6, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.3, predicted=-0.3
>expected=-0.3, predicted=-0.3
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=-0.4
>expected=-0.0, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.0, predicted=-0.0
>expected=0.7, predicted=1.4
>expected=1.2, predicted=1.3
>expected=0.4, predicted=0.7
>expected=1.5, predicted=1.1
>expected=1.3, predicted=1.4
>expected=-0.3, predicted=-0.1
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=0.9, predicted=0.5
>expected=0.9, predicted=1.3
>expected=-0.7, predicted=0.8
>expected=-0.0, predicted=0.8
>expected=-0.1, predicted=0.9
>expected=-0.1, predicted=-0.1
>expected=0.1, predicted=-0.0
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.4
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.1
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.3
>expected=-0.2, predicted=-0.1
>expected=-0.0, predicted=-0.1
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.217350 0.437233 0.546804 0.546804 0.896036
1 XGBoost 0.174098 0.352609 0.705255 0.705255 0.928531
2 SVM 0.197488 0.294435 0.794487 0.794487 0.952273
3 Random Forest 0.234018 0.418015 0.585768 0.585768 0.906890
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Min Flow')
plt.show()
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In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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10. RUNOFF (m3/s) ANALYSIS¶

In [ ]:
# Get the wind_min values
runoff = transformed_data[transformed_data['Parameter'] == parameters[4]]
runoff.head()
Out[ ]:
Parameter Date Value
4 Runoff 1995-01-01 2.340
9 Runoff 1996-01-01 62.878
14 Runoff 1997-01-01 4.414
19 Runoff 1998-01-01 10.213
24 Runoff 1999-01-01 12.164
In [ ]:
# drop the parameter columns
runoff = runoff.drop(columns=['Parameter'])
In [ ]:
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 2.340
9 1996-01-01 62.878
14 1997-01-01 4.414
19 1998-01-01 10.213
24 1999-01-01 12.164
In [ ]:
# sort according to  the date
runoff = runoff.sort_values(by='Date')
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 2.340
138 1995-02-01 2.553
272 1995-03-01 2.604
406 1995-04-01 10.093
540 1995-05-01 17.491
In [ ]:
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 2.340
138 1995-02-01 2.553
272 1995-03-01 2.604
406 1995-04-01 10.093
540 1995-05-01 17.491
In [ ]:
plt.figure(figsize=(20, 8))
runoff.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#ff7f0e', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Runoff (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
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In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(runoff['Value'])

ADF Test Statistic : -2.5872651063173273
p-value : 0.0956579797880519
#Lags Used : 11
Number of Observations Used : 300
Weak evidence against the null hypothesis(H0)
In [ ]:
runoff = runoff[['Date', 'Value']]
runoff.set_index('Date', inplace=True)
runoff.head()
Out[ ]:
Value
Date
1995-01-01 2.340
1995-02-01 2.553
1995-03-01 2.604
1995-04-01 10.093
1995-05-01 17.491
In [ ]:
runoff_model_names = []
runoff_mae_values = []
runoff_rmse_values = []
runoff_r2_values = []
runoff_nse_values = []
runoff_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `runoff` is your time series DataFrame
series = runoff
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Runoff (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=0.5, predicted=0.4
>expected=0.3, predicted=0.1
>expected=0.2, predicted=0.5
>expected=-0.5, predicted=-0.4
>expected=-0.6, predicted=0.0
>expected=-0.5, predicted=-0.1
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=0.1
>expected=0.3, predicted=0.2
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.2
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.2
>expected=0.0, predicted=-0.1
>expected=0.5, predicted=0.5
>expected=0.3, predicted=0.3
>expected=0.2, predicted=-0.2
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.1
>expected=-0.5, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=-0.1
>expected=0.3, predicted=0.3
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.5
>expected=-0.2, predicted=-0.0
>expected=0.0, predicted=-0.2
>expected=0.5, predicted=0.4
>expected=0.3, predicted=0.0
>expected=0.2, predicted=-0.0
>expected=-0.5, predicted=-0.3
>expected=-0.6, predicted=-0.3
>expected=-0.5, predicted=-0.2
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.5
>expected=0.3, predicted=0.2
>expected=0.3, predicted=0.0
>expected=0.4, predicted=0.1
>expected=-0.4, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.3
>expected=0.0, predicted=-0.3
>expected=0.5, predicted=0.5
>expected=0.3, predicted=0.1
>expected=0.2, predicted=0.2
>expected=-0.5, predicted=-0.4
>expected=-0.6, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=0.1
>expected=0.3, predicted=0.3
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.1
>expected=-0.2, predicted=-0.2
>expected=0.0, predicted=-0.2
>expected=0.5, predicted=0.4
>expected=0.3, predicted=0.1
>expected=0.2, predicted=0.5
>expected=-0.5, predicted=-0.4
>expected=-0.6, predicted=0.0
>expected=-0.5, predicted=-0.1
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=0.1
>expected=0.3, predicted=0.2
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.2
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.2
>expected=0.0, predicted=-0.1
>expected=0.5, predicted=0.5
>expected=0.3, predicted=0.3
>expected=0.2, predicted=-0.2
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.1
>expected=-0.5, predicted=0.2
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=-0.1
>expected=0.3, predicted=0.3
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.5
>expected=-0.2, predicted=-0.0
>expected=0.0, predicted=-0.2
>expected=0.5, predicted=0.4
>expected=0.3, predicted=0.0
>expected=0.2, predicted=-0.0
>expected=-0.5, predicted=-0.3
>expected=-0.6, predicted=-0.3
>expected=-0.5, predicted=-0.2
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.5
>expected=0.3, predicted=0.2
>expected=0.3, predicted=0.0
>expected=0.4, predicted=0.1
>expected=-0.4, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.3
>expected=0.0, predicted=-0.3
>expected=0.5, predicted=0.4
>expected=0.3, predicted=0.1
>expected=0.2, predicted=0.1
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.3
>expected=-0.5, predicted=0.1
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=0.3, predicted=0.0
>expected=0.3, predicted=0.3
>expected=0.4, predicted=0.3
>expected=-0.4, predicted=-0.4
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.6, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.4, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.3, predicted=-0.2
>expected=-0.2, predicted=-0.3
>expected=0.0, predicted=-0.2
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EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.112303 0.170880 0.788446 0.788446 0.941741
1 XGBoost 0.126930 0.205061 0.695349 0.695349 0.912229
2 SVM 0.140481 0.178119 0.770143 0.770143 0.917059
3 Random Forest 0.101752 0.155099 0.825717 0.825717 0.948409
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Runoff (m3/s)')
plt.show()
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In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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The End¶